Distinguishing ordinal and disordinal interactions

Area of Science:

• Statistics
• Psychology
• Developmental Science

Background:

• Standard regression models often struggle to test complex theoretical predictions involving interactive effects.
• Re-parameterization offers a novel approach to analyze interactions not directly testable with conventional methods.

Purpose of the Study:

• To introduce a re-parameterized regression model for analyzing Linear × Linear interactions between quantitative predictors.
• To extend this model for Linear × Qualitative interactions and moderating effects.
• To provide direct evidence for distinguishing ordinal from disordinal interactions.

Main Methods:

• Developed a re-parameterized regression model focusing on the crossover point of predicted values for Linear × Linear interactions.
• Generalized the model to accommodate qualitative variables (2 or 3 categories).
• Applied the models to social skills data from the National Institute of Child Health and Human Development Study of Early Child Care (N=438).

Main Results:

• The re-parameterized model yielded point and interval estimates for the crossover point near the mean of the continuous environment measure.
• Analysis revealed a disordinal interaction, not an ordinal one.
• The findings supported the differential-susceptibility theoretical model over a competing ordinal interaction model.

Conclusions:

• Re-parameterized regression models offer a powerful tool for testing nuanced theoretical predictions about interactions.
• The developed method effectively distinguishes between ordinal and disordinal interactions.
• Empirical application demonstrated the utility of the approach in developmental psychology research.